There are a few layers to the answer.
1. In the first approximation, it is an ellipse, considering that the central body is much more massive than the spacecraft.
2. When all influences (perturbations) are considered, the transfer can no longer be considered part of an ellipse, but ballistics chaps try to take into account most sources of perturbations, hence in an ideal world where all the uncertainties have been eliminated, transfer can be calculated.
3. Alas, there's no ideal world, so mid-course corrections are always planned (but not always executed if the margin of error is still acceptable).
4. Hohmann transfers may not always be preferable because of longish flight times, thus hyperbolic transfers may sometimes be used. If your spacecraft is a solar sail light enough, or has other sources of continuous thrust, optimal transfers will no longer be Keplerian (neither ellipse, nor parabola, nor hyperbola).
